1) Find the following z values for the standard normal variable Z. Use Table 1. (Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.)
a. P(Z ≤ z) = 0.8605
b. P(Z > z) = 0.8018
c. P(-z ≤ Z ≤ z) = 0.86
d. P(0 ≤ Z ≤ z) = 0.2235
2) Let X be normally distributed with mean μ = 20 and standard deviation σ = 12. Use Table 1.
a. Find P(X ≤ 2). (Round "z" value to 2 decimal places and final answer to 4 decimal places.)
P(X ≤ 2)
b. Find P(X > 5). (Round "z" value to 2 decimal places and final answer to 4 decimal places.)
P(X > 5)
c.Find P(5 ≤ X ≤ 20). (Round "z" value to 2 decimal places and final answer to 4 decimal places.)
P(5 ≤ X ≤ 20)
d. Find P(8 ≤ X ≤ 20). (Round "z" value to 2 decimal places and final answer to 4 decimal places.)
P(8 ≤ X ≤ 20)
3) Let X be normally distributed with mean μ = 125 and standard deviation σ = 29. Use Table 1.
a. Find P(X ≤ 100). (Round "z" value to 2 decimal places and final answer to 4 decimal places.)
P(X ≤ 100)
b. Find P(95 ≤ X ≤ 110). (Round "z" value to 2 decimal places and final answer to 4 decimal places.)
P(95 ≤ X ≤ 110)
c. Find x such that P(X ≤ x) = 0.440. (Round "z" value and final answer to 2 decimal places.)
x =
d. Find x such that P(X > x) = 0.900. (Round "z" value and final answer to 2 decimal places.)
x =
4) The average high school teacher annual salary is $43,000 (Payscale.com, August 20, 2010). Let teacher salary be normally distributed with a standard deviation of $18,000. Use Table 1.
a. What percentage of high school teachers make between $40,000 and $50,000? (Round "z" value and final answer to 2 decimal places.)
Percentage of high school teachers % =
b. What percentage of high school teachers make more than $80,000? (Round "z" value and final answer to 2 decimal places.)
Percentage of high school teachers % =n: 03_22_2016_QC_CS-46434
5) The time required to assemble an electronic component is normally distributed with a mean and a standard deviation of 29 minutes and 11 minutes, respectively. Use Table 1.
a. Find the probability that a randomly picked assembly takes between 18 and 30 minutes. (Round "z" value to 2 decimal places and final answer to 4 decimal places.)
Probability =
b. It is unusual for the assembly time to be above 44 minutes or below 16 minutes. What proportion of assembly times fall in these unusual categories? (Round "z" value to 2 decimal places and final answer to 4 decimal places.)
Proportion of assembly times =